EP2605420A1 - Method for separating electromagnetic emissions produced by a plurality of emitters - Google Patents

Abstract

The method involves acquiring electromagnetic signals from different sources, and determining a similarity criterion from measurement of a polarization of the electromagnetic signals. The criterion of similarity is used for clustering data. The similarity criterion is determined on the polarization from two detection measurements of the electromagnetic signals received on a sensor network using a statistical distance of Mahalanobis. The similarity criterion is determined by introducing a noise mode between two polarization measurements separated by a time.

Description

The object of the invention relates to a method and a system for separating electromagnetic emissions from several transmitters or sources in the field of telecommunications or in the field of radars.

One of the technical problems when one is in the presence of several emitting sources is to separate them and then to group the elementary detections by emission, that is to say to realize a segmentation of the measurements by unsupervised classification more known by the Anglo-Saxon acronym "clustering". It is therefore necessary to be able to separate the emissions coming from several emitting sources and received on several sensors or an antenna network.

The prior art describes several methods for separating signals from multiple sources or transmitters.

For example, the blind separation of sources consists of estimating a set of N sources from a set of P observations that are mixtures of these sources. The term blind means in this context that we do not know the signals a priori.

It is also known to perform the separation of signals using the parameters such as the frequency, the measurement instants, the directions of arrival. The method implemented in the prior art is known as the "unsupervised classification".

The techniques used in the prior art give good results. However, they have certain disadvantages including an inability to separate two similar electromagnetic emissions even if they are of different polarization, Indeed, as they do not exploit the polarization measurements, a confusion is possible between two different polarization emissions, if they also have relatively similar characteristics.

The object of the invention is in particular to provide a method for separating detections from two near or similar emissions, if their polarization is different, this by exploiting the polarization of the electromagnetic emissions received on a sensor.

• acquérir des signaux électromagnétiques issus de plusieurs sources distinctes,
• déterminer un critère de similarité à partir de la mesure de la polarisation desdits signaux électromagnétiques,
• utiliser ledit critère de similarité dans une méthode de classification non supervisée de données.

The invention relates to a method for deinterleaving electromagnetic signals received on a network of sensors positioned on a carrier, said sensor network being associated with a signal processing module comprising in combination at least the following steps:

• acquire electromagnetic signals from several different sources,
• determining a similarity criterion from the measurement of the polarization of said electromagnetic signals,
• using said similarity criterion in a method of unsupervised classification of data.

où V_i, V_j sont les paramètres de polarisation des détections D_i, D_j ; M_i,M_j les matrices de covariance associées ;
les mesures de polarisation correspondant à D_i, D_j sont données, par un vecteur de polarisation complexe (α, ϕ) : $$V_i=\left[\begin{array}{c}{\alpha }_i\\ {\phi }_i\end{array}\right]$$

paramètres de polarisation de la détection D_i $$V_j=\left[\begin{array}{c}{\alpha }_j\\ {\phi }_j\end{array}\right]$$

paramètres de polarisation de la détection D_j l'exposant ^T est le signe de transposé et l'indice _M est la signification de Mahalanobis
et ensuite en calculant une mesure de similarité en polarisation par la formule: $$s\left(V_1{V}_2\right)=\max \left\{\begin{array}{cc}0,& 1-\beta \mathrm{.}\sqrt{{\left(V_1-V_2\right)}^T{\left(M_1+M_2\right)}^{-1}\left(V_1-V_2\right)}\end{array}\right\}$$

According to one embodiment, corresponds to a fixed sensor configuration, the similarity criterion on the polarization is determined from two detection measurements D ₁ and D ₂ of the electromagnetic signals received on the sensor array using the statistical distance of Mahalanobis $${d^2}_M={\left(V_i-V_j\right)}^T{\left(M_i+M_j\right)}^{-1}\left(V_i-V_j\right)$$

where V _i , V _j are the polarization parameters of the detections D _i , D _j ; M _i , M _j the associated covariance matrices;
the polarization measurements corresponding to D _i , D _j are given by a complex polarization vector (α, φ): $$V_i=\left[\begin{array}{c}{\alpha }_i\\ {\phi }_i\end{array}\right]$$

polarization parameters of the detection D _i $$V_j=\left[\begin{array}{c}{\alpha }_j\\ {\phi }_j\end{array}\right]$$

polarization parameters of the detection D _j the exponent ^T is the sign of transposed and the index _M is the meaning of Mahalanobis
and then calculating a similarity measure in polarization by the formula: $$s\left({\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">V</figure-callout>}}_1{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0001.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\right)=\max \left\{\begin{array}{cc}0,& 1-\beta \mathrm{.}\sqrt{{\left(V_1-V_2\right)}^T{\left({\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">M</figure-callout>}}_1+M_2\right)}^{-1}\left(V_1-{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0001.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\right)}\end{array}\right\}$$

entre deux mesures de polarisation V1 et V2 séparées par une durée T, prenant en compte l'évolution de l'inclinaison de l'ellipse entre les deux mesures : en déterminant la covariance du bruit de modèle $$M_b=\left[\begin{array}{cc}{\sigma }_b^2& 0\\ 0& 0\end{array}\right]$$

covariance du bruit de modèle
avec un écart-type $$\begin{array}{c}{\sigma }_b^2\end{array}=\frac{1}{4}\begin{array}{c}{\mathit{da}}_{\max }^2\end{array}\mathrm{.}{T}^2+\begin{array}{c}{\sigma }_{\omega }^2\end{array}$$

et en calculant la distance statistique de Mahalanobis étendue en introduisant la covariance Mb du bruit de modèle : $$s\left(V_1{V}_2\right)=\max \left\{\begin{array}{cc}0,& 1-\alpha \mathrm{.}\sqrt{{\left(V_1-V_2\right)}^T{\left(M_1+M_2+M_b\right)}^{-1}\left(V_1-V_2\right)}\end{array}\right\}$$

According to another embodiment, corresponding to a slightly mobile sensor, the attitude position variations of the antenna array remaining small vis-à-vis the intercepted transmitter, the similarity criterion is determined by introducing a pattern noise $\tilde{b}=\left[\begin{array}{c}0\\ 0\end{array}\right]$

between two polarization measurements V1 and V2 separated by a duration T, taking into account the evolution of the inclination of the ellipse between the two measurements: determining the covariance of the noise model $$M_b=\left[\begin{array}{cc}{\mathrm{<figure-callout\; id="2"\; label="\sigma \; b"\; filenames="imgf0001.png"\; state="\{\{state\}\}">\sigma \; </figure-callout>}}_b^{}& 0\\ 0& 0\end{array}\right]$$

covariance of pattern noise
with a standard deviation $$\begin{array}{c}{\sigma }_b^{}\end{array}$$$$\begin{array}{c}{}_2^{}\end{array}=\frac{1}{4}\begin{array}{c}{\mathit{da}}_{\max }^2\end{array}\mathrm{.}{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="imgf0001.png"\; state="\{\{state\}\}">T</figure-callout>}}^2+\begin{array}{c}{\mathrm{<figure-callout\; id="2"\; label="\sigma \; \omega "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\sigma \; </figure-callout>}}_{\omega }^{}\end{array}$$

and calculating the extended Mahalanobis statistical distance by introducing the Mb covariance of the model noise: $$\mathrm{<figure-callout\; id="1"\; label="s\; V"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">s\; </figure-callout>}\left(V_{}\right)\left({}_1{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0001.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\right)=\max \left\{\begin{array}{cc}0,& 1-\alpha \mathrm{.}\sqrt{{\left(V_1-V_2\right)}^T{\left({\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">M</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="imgf0001.png"\; state="\{\{state\}\}">M</figure-callout>}}_2+M_b\right)}^{-1}\left(V_1-{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0001.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\right)}\end{array}\right\}$$

According to a third mode, adapted to situations where the sensor is highly mobile, a first step in determining the similarity criterion consists in correcting the tilt measurement of the polarization ellipse by taking into account the navigation information of the wearer, doing a change of reference of the plane of polarization, by a rotation in the plane of polarization making it possible to pass from the reference [u _h u _v ] linked to the calibrated antenna array and to the attitude to the reference [u ' _h u' _v ] linked to the horizontal of the place, and in a second step to calculate $$s\left({\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">V</figure-callout>}}_1{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0001.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\right)=\max \left\{\begin{array}{cc}0,& 1-\beta \mathrm{.}\sqrt{{\left(V_1-V_2\right)}^T{\left({\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">M</figure-callout>}}_1+M_2\right)}^{-1}\left(V_1-{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0001.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\right)}\end{array}\right\}\mathrm{.}$$

The method according to the invention is applicable, for example, for telecommunications signals to be deinterlaced or for radar signals.

The invention also relates to a device for deinterleaving electromagnetic signals received on an antenna array, said antenna array being associated with a signal processing module adapted to perform the steps of the method having the aforementioned characteristics.

• la figure 1 représente un exemple d'architecture permettant la mise en oeuvre du procédé selon l'invention,
• la figure 2, une représentation de la modélisation de la polarisation en réception,
• la figure 3, une modélisation de la prise en compte de la mesure de polarisation selon l'invention,
• les figures 4 et 5, un exemple de mise en oeuvre du procédé selon l'invention dans un traitement de segmentation COMINT.

Other features and advantages of the device according to the invention will appear better on reading the description which follows of an example of embodiment given by way of illustration and in no way limiting attached to the figures which represent:

• the figure 1 represents an example of an architecture allowing the implementation of the method according to the invention,
• the figure 2 , a representation of the modeling of the polarization in reception,
• the figure 3 , a modeling of the taking into account of the polarization measurement according to the invention,
• the figures 4 and 5 an example of implementation of the method according to the invention in a COMINT segmentation process.

In order to better understand the subject of the invention, the description given below relates to a method for separating electromagnetic emissions for telecommunications signals.

The figure 1 schematically an example of a system for carrying out the method according to the invention. Several sources emit signals in different directions. A sensor or a network of sensors associated with a data processing device receives the signals emitted by the different sources 10i or E.

An example of a general architecture of the transmission interception and location equipment of the transmitters according to the invention is represented in FIG. figure 1 . It comprises an antenna array 1, a reception device 2, a signal acquisition circuit 3, a data extraction and processing module 4. The antenna array is for example arranged on a carrier 5 locatable by its position and its attitude.

The antenna array 1 receives a set of signals from transmitters that are to be differentiated. The objective is notably to separate the signals received on the antennal system, to group the elementary detections by emission, that is to say to realize a segmentation of the measurements by unsupervised classification, better known under the Anglo-Saxon term " clustering ".

The idea implemented by the method according to the invention consists in particular in exploiting the measurement of polarization as an additional criterion of similarity in the unsupervised classification processing, known to those skilled in the art.

In order to better understand the object of the invention, a reminder on the measurement of the polarization will be given to the figure 2 .

The polarization measurement is a complex factor estimate near the Jones J vector , well known to those skilled in the art. This vector makes it possible to characterize the behavior of the electric field E of a monochromatic plane wave in the wave plane 20 (polarization plane) orthogonal to the wave vector k.

$${\mathrm{P}}_{\mathrm{v}}\mathrm{=}\mathrm{sin\alpha }{\mathrm{e}}^{\mathrm{j\phi }}$$

où α, abs(ϕ) (valeur absolue de ϕ) et signe(ϕ) définissent respectivement l'inclinaison, l'angle d'ellipticité et le sens de parcours de l'ellipse de polarisation dans le référentiel [u_h u_v ].
La mesure de polarisation est supposée donnée par l'estimation du vecteur unitaire p = [p_h p_v]' ou de façon équivalente par le rapport complexe P_v / P_h (=tanαe ^jϕ) ou encore par le couple (α, ϕ) (ou par le vecteur v = [α ϕ]').
La précision de la mesure de polarisation est supposée décrite par une matrice de covariance sur les paramètres (α, ϕ).In general, the end of the vector E describes, as a function of time in the plane of polarization, an ellipse 30, figure 3 , characterized in a reference [u _h u _v ], by an inclination α, a half minor axis a, a half major axis b and a direction of travel. The estimate of the Jones vector to a close complex factor can be characterized by a unit vector p of components p _h and p _v such that: $${\mathrm{P}}_{\mathrm{h}}\mathrm{=}\mathrm{cos\; \alpha }$$

$${\mathrm{P}}_{\mathrm{v}}\mathrm{=}\mathrm{sina}{\mathrm{e}}^{\mathrm{j\phi }}$$

where α, abs (φ) (absolute value of φ) and sign (φ) respectively define the inclination, the ellipticity angle and the direction of travel of the polarization ellipse in the repository [ u _h u _v ] .
The polarization measurement is assumed given by the estimation of the unit vector p = [p _h p _v ] 'or equivalently by the complex ratio P _v / P _h (= tanαe ^jφ ) or by the pair (α, φ ) (or by the vector v = [α φ] ').
The accuracy of the polarization measurement is supposed to be described by a covariance matrix on the parameters (α, φ).

The choice of the base [ u _h u _v ] as a geometric reference is arbitrary but linked to the reference frame of the antenna or antennal network. Considering that u _h characterizes the linear polarization propagating in the plane [ u _h k ] and that u _v characterizes the linear polarization propagating in the plane [ ku _v ], we observe that the vector p represents the decomposition of the field E in the orthonormal basis [ u _h u _v ]. By misuse of language, the polarizations P _h and Pv, the horizontal and vertical components, are denominated respectively, although they are really so only when the reference of the antenna or antennal network coincides with the horizontal and the vertical of the place ( ie in embedded context when the attitude of the wearer is horizontal) and when the wave propagates in the horizontal plane.

The figure 3 schematizes a representation of the use of the polarization measurement in the de-interlacing of the signals received on the receiver of the figure 1 several examples of which will be detailed below.

The figure 4 describes an example of implementation of the method in a COMINT segmentation processing and a way of taking into account the additional polarization criterion resulting from polarization measurements.

A typical COMINT segmentation processing is to perform a frequency histogram on the detection-goniometry data elementary plots, 400, and then separating the fixed frequency (FF) type emissions, 401, pulsed type or "bursts" EB, 402 emissions, based on a criterion of frequency occupancy. The FF pads are then transmitted to a first FF processing chain which will perform, for each of the active frequencies, an azimuth histogram 404 making it possible to consolidate the grouping on arrival direction criterion DOA, for example, and to validate the FF tracks. 405.

Emissions of the EB type are transmitted to a second processing chain, 402, which will segment EVF evasion emissions, 406, as well as isolated burst emissions based on DOA arrival direction criteria (histogram in azimuth), then estimation of the jump frequencies 407, and 408 step durations, in order to complete the segmentation in duration and synchronization using histograms. The classes obtained are then fused and synthesized for the preparation of FF, EVF and EB synthesis pads 410, 411, 412, respectively, using methods known to those skilled in the art.

The polarization criterion can be taken into account on the classes obtained following the azimuth histograms by introducing, for example, a polarization histogram calculation, or a partitioning based on the polarization similarity measurement (a definition of the polarization similarity criterion is given later in the description), in order to group in the same class as polarization-compatible polarization detections. The addition of this segmentation step on polarization criterion 504b, 506b, is illustrated on the figure 5 .

The polarization of the transmitter (ie the emission source) is assumed to be constant. However, it is necessary to take into account the variations of the polarization measurement between successive measurements caused by the possible movements of the carrier. The variation between two measurements of polarization of the same emission made at two times substantially spaced apart is caused by both the evolution of the geometrical configuration (angular scrolling of the carrier of the antennal network causing a variation of the incidence of the wave vector and thus a variation of the perceived polarization which can be seen as a projection of the polarization of the transmitter in the received wave plane) and by the attitude changes of the wearer (causing a rotation of the [ u _h u _v ] mark in the plane of polarization, which affects the tilt measurement of the polarization ellipse).

According to a first variant embodiment, the method is used on fixed transmitters in the case of receivers or interceptors of transmitted signals fixed on the carrier. The method uses a "raw" polarization measurement.

paramètres de polarisation de la détection D₁ $$V_{\mathit{2}}=\left[\begin{array}{c}{\alpha }_2\\ {\phi }_2\end{array}\right]$$

paramètres de polarisation de la détection D₂ Taking the polarization measurement into account in order to compare two detections results in considering a criterion of similarity of polarization based on the Mahanalobis distance, well known to those skilled in the art. Consider two detections D ₁ and D ₂ of the electromagnetic signals on the antenna array, the polarization measurements corresponding to these detections are given, for example, by a complex polarization vector (α, φ): $${\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">V</figure-callout>}}_{\mathit{1}}=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="\alpha "\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_1\\ {\mathrm{<figure-callout\; id="1"\; label="\phi "\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\phi </figure-callout>}}_1\end{array}\right]$$

polarization parameters of the detection D ₁ $$V_{\mathit{2}}=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="2"\; label="\alpha "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_2\\ {\mathrm{<figure-callout\; id="2"\; label="\phi "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\phi </figure-callout>}}_2\end{array}\right]$$

polarization parameters of detection D ₂

• M₁ la matrice de covariance associée à (V₁ )
• M₂ la matrice de covariance associée à (V₂ )

The covariance matrices associated with the polarization measurements (assumed Gaussian) are determined by methods known to those skilled in the art. Let

• M ₁ the covariance matrix associated with ( V ₁ )
• M ₂ the covariance matrix associated with ( V ₂ )

If the measurements on the inclination and eccentricity of the polarization ellipse are decorrelated, the covariance matrix is reduced to the associated standard deviations σ _α , σ _φ .

By definition in this first case, the relative variations of position and attitude of the antennal network of the receiver vis-à-vis an issuer are assumed negligible in view of the lower value of the estimation precisions of the polarization inclination max (σ _{α 1} , σ _{α 2} ). This makes it possible to consider that the relative incidences of the waves received, and therefore the wave vectors, are identical.

où V_i, V_j sont les paramètres de polarisation des détections D_i, D_j ; M_i,M_j les matrices de covariance associées ;
l'exposant T est le signe de transposé et l'indice M est la signification de MahalanobisIn the case of a fixed sensor configuration, the similarity criterion in polarization is expressed using the statistical distance of Mahalanobis known to those skilled in the art: $${d^2}_M={\left(V_i-V_j\right)}^T{\left(M_i+M_j\right)}^{-1}\left(V_i-V_j\right)$$

where V _i , V _j are the polarization parameters of the detections D _i , D _j ; M _i , M _j the associated covariance matrices;
the exponent T is the sign of transposed and the index M is the meaning of Mahalanobis

où $$s\left(V_1{V}_2\right)=\max \left\{\begin{array}{cc}0,& 1-\beta \mathrm{.}\sqrt{{d^2}_M}\end{array}\right\}$$

où β est un coefficient d'ajustement qui est fixé en choisissant un seuil sur la distance de Mahanalobis. Ce seuil se définit généralement à partir d'une probabilité de non association de mesures portant sur la même entité (le seuil se calcul à partir de cette probabilité d en utilisant la fonction de répartition de la distance de Mahanalobis qui suit une loi du chi2).This statistical distance of Mahalanobis then makes it possible to define a measure of similarity in polarization given by the formula: $$s\left({\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">V</figure-callout>}}_1{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0001.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\right)=\mathrm{<figure-callout\; id="0"\; label="max"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">max</figure-callout>}\left\{\begin{array}{cc}0,& 1-\beta \mathrm{.}\sqrt{{\left(V_1-V_2\right)}^T{\left({\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">M</figure-callout>}}_1+M_2\right)}^{-1}\left(V_1-{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0001.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\right)}\end{array}\right\}$$

or $$s\left({\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">V</figure-callout>}}_1{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0001.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\right)=\mathrm{<figure-callout\; id="0"\; label="max"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">max</figure-callout>}\left\{\begin{array}{cc}0,& 1-\beta \mathrm{.}\sqrt{{d^2}_M}\end{array}\right\}$$

where β is an adjustment coefficient which is fixed by choosing a threshold over the distance of Mahanalobis. This threshold is generally defined from a probability of non-association of measurements relating to the same entity (the threshold is calculated from this probability d by using the Mahanalobis distance distribution function that follows a Chi2 law). .

This polarization similarity measure is then exploited in the separation and clustering process of electromagnetic emissions as an additional criterion for unsupervised classification.

It can be, for example, either by contribution to the definition a global multicriteria similarity on the detections which will thus include the polarization, either simply as a new criterion implemented on the classes obtained after unsupervised classification based on the classical criteria (cascading of the criteria). In the latter case, if the polarization measurement accuracies are approximately constant and homogeneous with each other, it may be advantageous to limit the algorithmic complexity introduced by the new partitioning criterion by favoring the use of histograms on the polarization measurements. whose pitch is fixed according to standard deviations of precision.

According to a second variant embodiment, the variations of position and attitude of the antenna array are small, but not negligible, compared with the measurement error of the polarization. These variations correspond, for example, the variations of attitude position of the antenna array remain weak vis-à-vis the intercepted transmitter. In this case, the method will introduce model noise to make comparisons between polarization measurements.

Considering a maximum angular travel speed damax, the attitude variation of the antennal network can be modeled by a centered angular standard deviation σ _ω . This variation of attitude will essentially affect the inclination measurement α.

$$M_b=\left[\begin{array}{cc}{\sigma }_b^2& 0\\ 0& 0\end{array}\right]$$

covariance du bruit de modèle avec un écart-type $$\begin{array}{c}{\sigma }_b^2\end{array}=\frac{1}{4}\begin{array}{c}{\mathit{da}}_{\max }^2\end{array}\mathrm{.}{T}^2+\begin{array}{c}{\sigma }_{\omega }^2\end{array}$$

σ _b est déterminé à partir de la vitesse de défilement angulaire maximum du porteur et de l'écart-type sur l'inclinaison.Between two polarization measurements V1 and V2 separated by a duration T, the method introduces a pattern noise b taking into account the evolution of the inclination of the ellipse between the two measurements: $$\tilde{b}=\left[\begin{array}{c}0\\ 0\end{array}\right]$$

$$M_b=\left[\begin{array}{cc}{\mathrm{<figure-callout\; id="2"\; label="\sigma \; b"\; filenames="imgf0001.png"\; state="\{\{state\}\}">\sigma \; </figure-callout>}}_b^{}& 0\\ 0& 0\end{array}\right]$$

covariance of model noise with a standard deviation $$\begin{array}{c}{\sigma }_b^{}\end{array}$$$$\begin{array}{c}{}_2^{}\end{array}=\frac{1}{4}\begin{array}{c}{\mathit{da}}_{\mathrm{<figure-callout\; id="2"\; label="max"\; filenames="imgf0001.png"\; state="\{\{state\}\}">max</figure-callout>}}^2\end{array}\mathrm{.}{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="imgf0001.png"\; state="\{\{state\}\}">T</figure-callout>}}^2+\begin{array}{c}{\mathrm{<figure-callout\; id="2"\; label="\sigma \; \omega "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\sigma \; </figure-callout>}}_{\omega }^{}\end{array}$$

σ _b is determined from the maximum angular travel speed of the carrier and the standard deviation on the inclination.

The polarization similarity criterion will then use an extended Mahalanobis statistical distance by introducing the covariance M _b of the model noise: $$s\left({\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">V</figure-callout>}}_1{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0001.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\right)=\mathrm{<figure-callout\; id="0"\; label="max"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">max</figure-callout>}\left\{\begin{array}{cc}0,& 1-\alpha \mathrm{.}\sqrt{{\left(V_1-V_2\right)}^T{\left({\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">M</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="imgf0001.png"\; state="\{\{state\}\}">M</figure-callout>}}_2+M_b\right)}^{-1}\left(V_1-{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0001.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\right)}\end{array}\right\}$$

If a polarization-based histogram-based partitioning method is preferred over a partitioning method using the Mahanalobis distance-based similarity measure, then model noise takes into account increase of the histogram step deduced from the standard deviation σ _b .

According to a third variant embodiment, adapted to situations where the sensor is highly mobile, for example when the value of the polarization observed is greatly modified by the position and / or attitude position variations of the carrier.

The method for this third implementation variant consists in limiting the effect of the position variations of the wearer by limiting the exploitation of the polarization measurement to the deinterleaving processes that take place over a limited horizon, typically a sensor cycle (over time). of a sensor cycle, which is of the order of magnitude of the second, the position variation of the carrier can be considered negligible in the case of measurement accuracies).

With regard to the attitude variations of the antennal network, considered as potentially important in the latter case (even on the horizon of a sensor cycle), the method relies on the use of navigation information delivered for example by a navigation center known to those skilled in the art and located on the carrier and on the choice of a mark [ u ' _h u' _v ] of the polarization plane which is wedged on the horizontal of the place and therefore independent of the attitude of the wearer .

The choice of such a marker involves correcting the tilt measurement of the polarization ellipse by taking into account the navigation information by performing a change of polarization plane mark (rotation in the polarization plane to pass from the reference [ u _h u _v ] linked to the calibrated antenna network and therefore to the attitude at the mark [ u ' _h u' _v ] related to the horizontal of the place). This benchmark then makes it possible to compare the corrected measures when the variation of the position of the carrier relative to the transmitter remains low.

The corrected polarization measurements are determined by the following formula, using the values of V1, V2, corrected by changing the reference: $$s\left({\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">V</figure-callout>}}_1{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0001.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\right)=\mathrm{<figure-callout\; id="0"\; label="max"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">max</figure-callout>}\left\{\begin{array}{cc}0,& 1-\beta \mathrm{.}\sqrt{{\left(V_1-V_2\right)}^T{\left({\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">M</figure-callout>}}_1+M_2\right)}^{-1}\left(V_1-{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0001.png"\; state="\{\{state\}\}">V</figure-callout>}}_2\right)}\end{array}\right\}$$

If a method of partitioning based on histograms is favored, the corrected measures are directly counted with a histogram step based on the standard deviations of measurement.

Claims (7)

Method for deinterleaving electromagnetic signals received on a network (1) of sensors positioned on a carrier (5), said sensor array being associated with a signal processing module (4) comprising in combination at least the following steps: • acquire electromagnetic signals from several different sources, Determining a similarity criterion from the measurement of the polarization of said electromagnetic signals, • use said similarity criterion in a method of unsupervised classification of data. Method according to Claim 1, characterized in that the polarization similarity criterion is determined from two detection measurements D ₁ and D ₂ of the electromagnetic signals received on the sensor array using the statistical distance of Mahalanobis. $${d^2}_M={\left(V_i-V_j\right)}^T{\left(M_i+M_j\right)}^{-1}\left(V_i-V_j\right)$$

where V _i , V _j are the polarization parameters of the detections D _i , D _j ; M _i , M _j the associated covariance matrices;
the polarization measurements corresponding to D _i , D _j are given by a complex polarization vector (α, φ): $$V_i=\left[\begin{array}{c}{\alpha }_i\\ {\phi }_i\end{array}\right]$$

polarization parameters of the detection D _i $$V_j=\left[\begin{array}{c}{\alpha }_j\\ {\phi }_j\end{array}\right]$$

polarization parameters of the detection D _j
the exponent ^T is the sign of transposed and the index _M is the meaning of Mahalanobis
and then calculating a similarity measure in polarization by the formula: $$s\left(V_1{V}_2\right)=\max \left\{\begin{array}{cc}0,& 1-\beta \mathrm{.}\sqrt{{\left(V_1-V_2\right)}^T{\left(M_1+M_2\right)}^{-1}\left(V_1-V_2\right)}\end{array}\right\}$$

Process according to Claim 1, characterized in that the similarity criterion is determined
by introducing a pattern noise $$\tilde{b}=\left[\begin{array}{c}0\\ 0\end{array}\right]$$

between two polarization measurements V1 and V2 separated by a duration T, taking into account the evolution of the inclination of the ellipse between the two measurements
determining the covariance of the model noise; $$M_b=\left[\begin{array}{cc}{\sigma }_b^2& 0\\ 0& 0\end{array}\right]$$

covariance of model noise with a standard deviation $$\begin{array}{c}{\sigma }_b^2\end{array}=\frac{1}{4}\begin{array}{c}{\mathit{da}}_{\max }^2\end{array}\mathrm{.}{T}^2+\begin{array}{c}{\sigma }_{\omega }^2\end{array},$$

and
calculating the extended Mahalanobis statistical distance by introducing the model noise covariance Mb: $$s\left(V_1{V}_2\right)=\max \left\{\begin{array}{cc}0,& 1-\alpha \mathrm{.}\sqrt{{\left(V_1-V_2\right)}^T{\left(M_1+M_2+M_b\right)}^{-1}\left(V_1-V_2\right)}\end{array}\right\}$$

Method according to Claim 2, characterized in that to determine the similarity criterion, A first step consists in correcting the tilt measurement of the polarization ellipse by taking into account the navigation information of the wearer, by making a change of reference of the plane of polarization, by a rotation in the plane of polarization allowing to go from the reference [u _h u _v ] linked to the calibrated antenna array and the attitude to the reference [u ' _h u' _v ] linked to the horizontal of the place, and • in a second step we calculate $$s\left(V_1{V}_2\right)=\max \left\{\begin{array}{cc}0,& 1-\beta \mathrm{.}\sqrt{{\left(V_1-V_2\right)}^T{\left(M_1+M_2\right)}^{-1}\left(V_1-V_2\right)}\end{array}\right\}\mathrm{.}$$

Method according to one of Claims 1 to 4, characterized in that the electromagnetic signals to be deinterleaved are telecommunications signals. Method according to one of Claims 1 to 4, characterized in that the electromagnetic signals to be deinterlaced are radar signals. Device for deinterleaving electromagnetic signals received on an antenna array (1), said antenna array being associated with a signal processing module (4) adapted to perform the steps of the method according to one of claims 1 to 6.

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